Logics

Traditional degree semantics approaches have aimed to pin down the inherent class of adjectives. This paper presents a novel dynamic perspective, where the classification of an adjective is dynamic and syntactically dependent. Using measurement theory and fuzzy set analysis, the proposed framework defines dynamic patterns of adjective classes with a set of axioms and integrates these patterns with syntactic structures to explain the flexibility and constraints observed in adjectival expressions. Employing Mandarin data, the paper illustrates how different syntactic constructions select specific adjective classes, thereby affecting their distribution and interpretation. This approach not only accommodates cross-linguistic variations but also provides a more comprehensive understanding of the semantics of adjectives.

We offer a framework that captures both context-dependency and vagueness of predicate meanings—illustrated by the politically relevant case of woman—as an interaction of lexical meaning and Question under Discussion (‘QUD’). We extend existing approaches to non-maximality to superficially polysemous predicates like woman and show that this is conceptually coherent and insightful for a linguistic analysis of political debates about gender invitation policies: while there are (i) clear, semantically true, and (ii) strictly unacceptable cases of x is a woman, there are also (iii) merely pragmatically acceptable cases (‘like a woman with respect to the QUD’) as well as (iv) truly vague ones. We argue that this four-way division is the least complex model that captures current gender discourses in a harm-reducing, trans-inclusive way. This offers a new perspective on the semantics–pragmatics interface of predicate meanings.

José Morgado introduced in 1962 a novel notion of hyperlattices, which he called reticuloides. In his master’s thesis submitted in 1971 (under the supervision of Newton da Costa), Antonio M. Sette introduced a new class of implicative hyperlattices (here called SIHLs) based on Morgado’s hyperlattices. He also extended SIHLs by adding a unary hyperoperator, thus defining a class of hyperalgebras (denoted ${\mathrm{SHC}}_{\omega }$) corresponding to da Costa algebras for $C_{\omega }$, thereby providing suitable semantics for the logic $C_{\omega }$. In this paper, after providing a (hyper)lattice-theoretic characterization of Sette’s implicative hyperlattices and proving some basic results on SIHLs, we introduce a class of swap structures—special hyperalgebras over the signature of $C_{\omega }$ that arise naturally from implicative lattices. We prove that these swap structures are indeed ${\mathrm{SHC}}_{\omega }$. Finally, we demonstrate that the class ${\mathrm{SHC}}_{\omega }$, as well as the aforementioned swap structures, characterizes the logic $C_{\omega }$.